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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2018, Volume 58, Number 7, Pages 1084–1088
DOI: https://doi.org/10.31857/S004446690000372-0 (Mi zvmmf10745) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A new proof of the Kuhn–Tucker and Farkas theorems

Yu. G. Evtushenkoa, A. A. Tret'yakovbac

a Dorodnitsyn Computing Centre, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow, Russia
b System Research Institute, Polish Academy of Sciences, Warsaw, Poland
c Faculty of Sciences, Siedlce University, Siedlce, Poland
Citations (1)
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DOI: https://doi.org/10.31857/S004446690000372-0
Abstract: For the minimization problem for a differentiable function on a set defined by inequality constraints, a simple proof of the Kuhn–Tucker theorem in the Fritz John form is presented. Only an elementary property of the projection of a point onto a convex closed set is used. The approach proposed by the authors is applied to prove Farkas’ theorem. All results are extended to the case of Banach spaces.
Key words: projection, Kuhn–Tucker theorem, convex hull, optimality conditions, local minimum.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 27
Received: 11.05.2017
Revised: 01.11.2017
English version:
Computational Mathematics and Mathematical Physics, 2018, Volume 58, Issue 7, Pages 1035–1039
DOI: https://doi.org/10.1134/S0965542518070072
Bibliographic databases:
Document Type: Article
UDC: 519.85
Language: Russian
Citation: Yu. G. Evtushenko, A. A. Tret'yakov, “A new proof of the Kuhn–Tucker and Farkas theorems”, Zh. Vychisl. Mat. Mat. Fiz., 58:7 (2018), 1084–1088; Comput. Math. Math. Phys., 58:7 (2018), 1035–1039
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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